Can an interval be spiraling on a graph?

campbell's paycheck was $358.60 she put 1/5 of her paycheck into a savings account use 1/2 of what she was left with to pay bill

Mice21 [21]

The final answer is circled

6 0

3 years ago

Let $$\mathbf { u } , \mathbf { v } , \text { and } \mathbf { w }$$ be vectors. Which of the following make sense, and which do

Daniel [21]

(u × v) • w makes sense, since u × v is another vector, and so (u × v) • w is a scalar.

u × (v • w) does not make sense, since v • w is a scalar, and the cross product is not defined between a vector and a scalar.

(u × v) × w makes sense, since u × v is a vector and so is w.

u • (v • w) does not make sense, since v • w is scalar, and the dot product is not defined between a vector and a scalar.

5 0

3 years ago

Matt is standing on top of a cliff 305 feet above a lake. The measurement of the angle of depression to a boat on the lake is 42

bonufazy [111]

Answer:

≈ 410.4427 feet (this is rounded -- it's an infinite decimal)

Step-by-step explanation:

If you draw it out, you get a right triangle. If Matt is standing 305 feet above a lake, that is the altitude of the triangle. The angle of depression means, for example, the angle looking down from something at something else, in this case, from the cliff to the boat. The 42° is the acute angle between the altitude and the hypotenuse, the one at the top of the triangle. You want to find how far away the boat is from Matt directly, so that would be the hypotenuse, just connecting a straight line from him to the boat.

To answer these problems there are three tools you use to find the answer: Sine, Cosine, and Tangent. Let's see which one would best help us in this situation.

The definition of sine is the side opposite the acute angle over the hypotenuse.

The definition of cosine is the side adjacent to the acute angle over the hypotenuse.

The definition of tangent is the side opposite the acute angle over the side adjacent to it.

In this case, you know you have the side adjacent to the acute angle, over the hypotenuse. Because you have the acute angle (42°) and the side adjacent to it (305) and the hypotenuse (which is what you're trying to find the value of. Which definition would fit this figure? Cosine, because it's side adjacent over hypotenuse.

Once you have that straightened out, you know that you need to find the cosine of 42°, which, if you look in a sine, cosine, and tangent chart (or type 42 into your calculator and hit cos) is 0.7431. Now you can write the equation $0.7431 = \frac{305}{x}$ .

Working with that equation, you need to get x by itself to figure out its value. How you do that is by multiplying both sides by x. This would look like $0.7431 * x = 305 * x$ . When you multiply 305 by x, you are multiplying by the number you were just dividing by so that answer is 305. I'll give you an example with different numbers: 6/2 then 6*2 is just 6.

What your equation looks like now is $0.7431 * x = 305$ . How do you find x? Well it's the same as doing this: $2 * x = 8$ . Then you would divide 8 by 2 to get x, which equals 4. So, going back to our task at hand, $305/0.7431 = x = 410.4427 (approximately)$ . That's your answer, which is how far Matt is from the boat. Depending on which digit they want you to round the answer to you could punch in 305/0.7431 into a calculator and see many more digits and a much longer number. But don't forget to include units in your answer -- feet.

6 0

3 years ago

There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh graders, and the rest are eighth grader

dalvyx [7]

Answer:

The band members of sixth graders are 28.

The band members of seventh graders are 14.

The percentage of the band members eighth graders are 40% .

Step-by-step explanation

Formula

$Percentage = \frac{Part\ value\times 100}{Total\ value}$

As given

There are 70 students in the school band.

40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.

Now first find out the band members are sixth graders .

Percentage = 40%

Total value = 70

Put in the formula

$40 = \frac{Number\ of\ band\ members\ are\ sixth\ graders\times 100}{70}$

$Number\ of\ band\ members\ are\ sixth\ graders = \frac{40\times 70}{100}$

$Number\ of\ band\ members\ are\ sixth\ graders = \frac{2800}{100}$

$Number\ of\ band\ members\ are\ sixth\ graders = 28$

Therefore the number of band members are from sixth graders are 28 .

Now first find out the band members are seventh graders .

Percentage = 20%

Total value = 70

$20 = \frac{Number\ of\ band\ members\ are\ seventh\ graders\times 100}{70}$

$Number\ of\ band\ members\ are\ seventh\ graders = \frac{20\times 70}{100}$

$Number\ of\ band\ members\ are\ seventh\ graders = \frac{1400}{100}$

$Number\ of\ band\ members\ are\ seventh\ graders = 14$

Therefore the number of band members are from seventh graders are 14.

Now find out the percentage of the eighth graders of the band members.

Total number of band members = sixth graders members + seventh grade members + eighth graders members

As sixth graders members = 28

seventh grade members = 14

Total number of band members = 70

Put in the above

70 = 28 + 14 + eighth graders members

70 - 42 = eighth graders members

28 = eighth graders members

Put in the percentage formula

$Percentage = \frac{28\times 100}{70}$

$Percentage = \frac{2800}{70}$

Percentage = 40%

Therefore the percentage of the band members are eighth graders is 40 %.

5 0

3 years ago

Can anyone please help!!!! QUESTION ATTACHED TO PICTURE

Mariulka [41]

Answer:

$D) y=-\frac{2}{3}x+ 2$

Step-by-step explanation:

$Equation ~ of ~ the ~ line~ is ~ y=mx+b\\\\m= slope\\\\b=y-intercept$

$to ~find ~ the ~ slope~ use ~ formula:-\\\\ slope=\frac{y_{2}-yx_{1} }{x_{2} -x_{1} } \\(0,2)(3,0)$

$slope=\frac{0-2}{3-0}$

$y-intercept ~ is (0,2) ~ so, b=2$

$The ~ equation ~ of ~ the ~ line~ is:- \\$

$y=-\frac{2}{3}x+2$

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hope it helps...

have a great day!!

4 0

2 years ago